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<p>Therefore, suppose (<a href="" class="xref" data-knowl="./knowl/eq5_17.html" title="Equation 5.5.7">(5.5.7)</a>) has two real roots <span class="process-math">\(r_1\)</span> and <span class="process-math">\(r_2\)</span> (<span class="process-math">\(r_1 \geq r_2\)</span>). Then, there exists a solution of the form</p>
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\begin{equation}
y_1=x^{r_1} \sum_{n=0}^{\infty} a_n x^n \quad \textrm{with}~a_0=1, \quad \textrm{for}~0&lt;x&lt;\rho.\tag{5.5.8}
\end{equation}
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